Quick Practice
Nina and Olga are two authors selling the books they individually published . The numbers of books sold by them in each year are investigated .
Part I – Models for the Population 1
The following table shows the number of books x , sold by Nina each year , where n is the number of years after 2000 :
n 1 2 3 4 5 7 9
x 400 380 365 350 348 357 311
( a ) The relationship between the variables is modelled by the regression equation
3 2 x( n) an bn cn d � � � � .
( 1 ) Write down the values of a , b , c and d .
( 2 ) Hence , estimate the number of books sold by Nina in 2006 , giving the answer correct to the nearest integer .
( 3 ) Comment the validity of this estimation .
( b ) Nina claims that the population mean � of the number of books sold by her from 2003 to 2012 is less than 370 . A one sample t -test is conducted at a 5 % significance level to test Nina ’ s claim .
20
( 1 ) Write down the exact value of the sample mean of the number of books sold from 2003 to 2012 .
( 2 ) Write down the null hypothesis of the test .
( 3 ) Write down the alternative hypothesis of the test .
( 4 ) Find the p -value .
( 5 ) State the conclusion of the test with a reason .
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